I tried to install darkice with lame. To compile it, I need ALSA and Pulsaudio:

checking for lame library at /usr ... found at /usr
checking for vorbis libraries at /usr ... configure: WARNING: not found, building without Ogg Vorbis
checking for opus libraries at /usr ... configure: WARNING: not found, building without Ogg Opus
checking for faac library at /usr ... configure: WARNING: not found, building without faac
checking for aacplus library at /usr ... configure: WARNING: not found, building without aacplus
checking for twolame library at /usr ... configure: WARNING: not found, building without twolame
checking for alsa libraries at /usr/lib/alsa-lib ... configure: WARNING: not found, building without ALSA support
checking for pulseaudio libraries at /usr/lib64/pulseaudio/libpulse ... configure: WARNING: not found, building without PULSEAUDIO support
checking for jack libraries at /usr ... configure: WARNING: not found, building without JACK support
checking for samplerate libraries at /usr ... configure: WARNING: not found, building libsamplerate support

I can add with --with-*-prefix= a path for this libraries. But I have no idea where on my system I can find them, or what I need to install, to compile with them.

Rather than attempt to compile this myself I'd be inclined to get the source RPM for lame and rebuild that. You can then lean on the package management software to assist in getting the necessary packages installed so that you can rebuild lame.

Start with getting an RPM development environment setup. Afterwards you'll need to download the lame source RPM. You'll then use the tool rpmbuild with the switch --rebuild and the lame source RPM to build it.

Everything you need is spelled out in this blog tutorial, titled: [Rpmbuild Tutorial].1. I've also written about it extensively on my blog in this series of posts.